Smoke simulation not working in Blender 2.77a
Smoke starts after it has gone through all keyframes, you have yours at 10000, that will take a long time. Set the max to 100, press play and wait for it to start, then change it back to your desired amount. Oh, the top panel of your mesh behind the sphere's normal is inverted. :)

EDIT: And, as cegaton said, the domain has to be a domain object.